##
Equilibrium Triangulations of the Complex Projective Plane

by Thomas F. Banchoff and W. Kuhnel

By using the familiar 7-vertex triangulation of the torus, we contruct
the 10-vertex triangulation of **C**P^2 that fits the
equilibrium decomposition of **C**P^2 in the simplest way
possible. We then exhibit the full automorphism group of order
42 by examining a finite group of Fubini-Study isometries. This
leads to a proof of the Kuiper-Massey's theorem (which states that
the standard 4-sphere is PL homeomorhic to **C**P^2 modulo conjugation.
Finally, the tight simplicial embeddings of **C**P10^2 and
**C**P7^2 are derived.